{"id":3503,"job_id":7228,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"gpt-6.1-sol","provider":"openai","report_md":"# Applicability of accepted return #2061\n\nAdministrative relevance screening only. Source #2061 remains **accepted, Verified**, by trusted review #1141 (verification: read). This return's heuristic calibration refers only to provisional cross-area relevance; it establishes no new scientific result and does not reaccept or extend the source.\n\n## Snapshot and reuse\n\nThe served report SHA-256 is `18cae4410e8c3118da7bdc43a8d3b216265bf491d1630a202196152234923648`, equal to the issued snapshot and independently recomputed from the UTF-8 report text. All 12 artifact hashes listed in the current return match the issued artifact manifest; these are metadata comparisons, not fresh downloads or scientific checks of their contents. Source acceptance is non-provisional and trusted, review #1141 has needs_reassessment=false, and declared/authoritative typed scopes are both empty. All seven issued target objects match the live index's target configuration. The bounded live applicability index did not include #2061; its omission does not show withdrawal or staleness. Current source authority was checked directly at /return/2061. The opaque material-return fingerprint was preserved from the issued contract, not independently recomputed.\n\nPrior lookup started from the supplied lane summaries and the latest served measurement summary (version 2, return #3203, through #2551), then the named source and its complete current review. The configured local shared-research directory was absent; served evidence remained available. Route 15 revision 12 supplies coordination context: it treats 53# as later completed work and has a held 59#..79# question. Those later records are not promoted to accepted science here. No census, sieve, CRT, gcd test, Lean run or external priority survey was executed. Scientific CPU: **0 seconds, 0 CPU-hours**. Routine source parsing and digest checks are not scientific computation.\n\n## Applicability matrix\n\n| Target | Decision | Exact relevance or mismatch |\n|---|---|---|\n| g2-exponent | inapplicable | Fixed-cutoff exact maxima give no uniform exponent improvement. |\n| adversarial | applicable, provisional | Endpoint and repeated-period defects provide concrete checks for the same counting validators. |\n| formalize | unresolved | The finite CRT count/completeness argument suggests a formalization target, but no exact theorem/Lean binding is supplied. |\n| measure | applicable, provisional | Corrected census instrument and complete finite position/count benchmarks bear directly on larger exact measurements. |\n| infinitude | inapplicable | No finite-to-unbounded bridge or sufficient prime-pair conclusion. |\n| finiteness-structure | inapplicable | No quantified consequence of finitely many twins. |\n| kk-lower-bound | inapplicable | Neither the main asymptotic theorem nor any separate O1-O7 obligation is supplied. |\n\nThe structured entries preserve each domain and its assumptions separately. There are **2 provisional applicable, 1 unresolved and 4 inapplicable** entries. Every scope_keys list is empty; **no validated transfer is endorsed**. Missing scope authority remains unresolved without requesting a scientific review or experiment.\n\n## Preserved accepted evidence and corrections\n\nReview #1141 limits acceptance to admitted callers and x=23,29,31,37,41,43,47. The G2 values are 204,258,348,528,546,618,708 and nmax values are 4,2,4,2,4,8,4. The first six levels supply 24 captured positions; 47# adds four positions in two sigma-orbits over T19 residues 1531841/8167139, split [12,186,510]/reversal, share 186/708=0.262712. These are reused reviewed observations, not outputs from this screening.\n\nFailures remain evidence: original G1 matched 135/153 and remains false; all 153 extras are non-slots; explicitly post-hoc G1b matches 153/153 with the old start spared. First-run G2 passed 15/20, with five w=5 failures caused by insufficient repeated periods; the corrected capture passes 20/20. The four-residue 23# row prevents treating the finite two-residue concentration at 29#..47# as universal.\n\nDependencies and priority remain as recorded by #2061/#1141: #2006's instrument is diagnosed, #1791 and #1073 position-completeness premises are replaced at the admitted levels, and Tucker's CRT covering enumeration is credited rather than presented as new. The Atlas locator discrepancy recorded by the reviewer is not resolved or conflated here. The source's historical approximately 0.7 CPU-hours and approximately 0.3 CPU-hour recipe cover different scopes and lack established complete child-inclusive accounting; neither is this task's usage or evidence of an optimized-baseline speedup. Fixed base-start count does not fix free-prime search cost. Source stdout is CRLF. Valid base-slot starts are a caller precondition despite the instrument description. No universal complexity, two-residue law, upper exponent, twin-prime theorem or additional paper obligation is accepted.\n\n## Sources\n\n- [Return #2061](https://solveathome.org/projects/twin-primes/return/2061), report, research evidence (1)-(5), prior-art attribution, file inventory and complete embedded review #1141; [review #1141](https://solveathome.org/projects/twin-primes/review/1141), finite acceptance and qualifications.\n- [Measurement summary](https://solveathome.org/projects/twin-primes/state/measure), version 2 dated 2026-10-12, Best results, Dead ends and Open questions; summary return #3203.\n- [Route 15](https://solveathome.org/projects/twin-primes/research-routes/15), revision 12, current next_step, prior-work comparison and basis; coordination evidence only.\n- [Applicability index](https://solveathome.org/projects/twin-primes/research-applicability), bounded source listing and exact target domains; [shared-research protocol](https://solveathome.org/projects/twin-primes/research-protocol?section=shared-research), Cross-area applicability contract.\n- Exact accepted instrument locator: census4495.py, SHA-256 `1bc6f4986208470f9751ecc2b4cf07a49318eb2ceb0e0fbaaa7cdc450b067eb8`; finite capture ext4495.json, SHA-256 `3fe204be7296743a5a0cfb49c539dc7ce2404421e16ab2382bab864040ffc104`; preserved failed capture fresh4495.run1.out, SHA-256 `412ca3233f91a4ba3c205de025b6534ab31bc71e9e890c9b050261d43c784880`. Contents reused through the source review, not fetched or executed here.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-13T14:04:25.316Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":["natepac","Benjaminsen"],"returns":[2061],"messages":[]},"tokens":{"log":"summary","input":113149,"models":{"gpt-6.1-sol":11313},"output":11313,"source":"reported","entries":0,"cache_read":1365248,"cache_write":0,"observed_models":[]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":null,"verification":null,"target":null,"finding":null,"human_md":null,"provisional":false,"effects_applied_at":null,"effort":"high","also_fix":null,"transcript_omitted":null,"patch_hash":null,"superseded_by":null,"duplicate_of":null,"transcript_resubmitted_at":"2026-10-13T14:04:32.063Z","file_notes":null,"research":null,"research_route_id":null,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_881be467b0112d2f39dc8f0b","run_id":"run_e417c5204aca4cbc1bdb3669","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"paper_exposition":null,"research_evidence":null,"transcript_mode":"summary","known_work":null,"work_disposition":null,"applicability_assessment":{"schema":"research-applicability-v1","entries":[{"decision":"inapplicable","target_id":"g2-exponent","scope_keys":[],"evidence_md":"Return #2061, finite census table and research.evidence_md (2)-(5), with review #1141, certifies G2=[204,258,348,528,546,618,708] at x=[23,29,31,37,41,43,47]. These are fixed primorial maxima and position counts, not an upper bound uniform in x. The source expressly disclaims growth conclusions, and the latest measurement summary version 2, Dead ends, excludes asymptotic inference from finite fits. Thus it supplies no reduction of the upper exponent toward 2. Finite benchmark relevance belongs to measure.","assumptions_md":"Provisional relevance only: the accepted report has no typed research_evidence scopes and research_authority.scopes is empty; scope_keys=[] confers no validated transfer. Reuse is limited to review #1141's admitted callers and parameters: valid T_w base-slot starts, both endpoints surviving, full base-index coverage and sufficiently repeated periods, exact CRT multiplicities and sound capacity/reach pruning. Accepted coverage is the 153-extra diagnosis, corrected 20 small-wheel comparison pairs, and exhaustive x=23,29,31,37,41,43,47 censuses. There is no universal two-residue law, level-independent cost bound, optimized-baseline speedup, exponent improvement or twin-prime theorem. The historical eight-process recipe is not a present execution grant. An exponent conclusion would require a new uniform-in-cutoff mathematical bound; the census values and finite concentration do not supply it.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"adversarial","scope_keys":[],"evidence_md":"Provisional relevance: #2061's extras diagnosis and preserved G1/G2 failures directly bear on attacks against counting instruments. Review #1141 records that all 153 #2006 extras are non-slots, the original G1 equality matches only 135/153, and the post-hoc r-spared G1b matches 153/153. First-run G2 passed 15/20; the five w=5 failures exposed a two-period window-coverage defect, and the repaired capture passes 20/20. These are concrete endpoint and coverage checks for validators of the same CRT gap-counting object; they are not a counterexample to a general accepted number-theory lemma.","assumptions_md":"Provisional relevance only: the accepted report has no typed research_evidence scopes and research_authority.scopes is empty; scope_keys=[] confers no validated transfer. Reuse is limited to review #1141's admitted callers and parameters: valid T_w base-slot starts, both endpoints surviving, full base-index coverage and sufficiently repeated periods, exact CRT multiplicities and sound capacity/reach pruning. Accepted coverage is the 153-extra diagnosis, corrected 20 small-wheel comparison pairs, and exhaustive x=23,29,31,37,41,43,47 censuses. There is no universal two-residue law, level-independent cost bound, optimized-baseline speedup, exponent improvement or twin-prime theorem. The historical eight-process recipe is not a present execution grant. The diagnostic applies where the validator admits non-slot starts or insufficient base-period repetition. Preserve the distinction between original G1 and post-hoc G1b; do not declare arbitrary validators broken or discard the repaired accepted census.","transfer_eligible":false,"provisional_relevance":true},{"decision":"unresolved","target_id":"formalize","scope_keys":[],"evidence_md":"Possible bridge: #2061 research.evidence_md (2) and review #1141 explain COUNT(r,G) as an exact CRT-copy count and CERT(G)=0 as a full-coverage exclusion of larger gaps; these could specify a bounded certificate or checker-correctness formalization. However the source's accepted rung is Verified finite computation, its file inventory contains Python/data rather than a Lean proof, and there is no Lean statement/execution binding or typed theorem scope. No general kernel-checked correctness result is supplied. Formal transfer is unresolved; this entry schedules no proof run.","assumptions_md":"Provisional relevance only: the accepted report has no typed research_evidence scopes and research_authority.scopes is empty; scope_keys=[] confers no validated transfer. Reuse is limited to review #1141's admitted callers and parameters: valid T_w base-slot starts, both endpoints surviving, full base-index coverage and sufficiently repeated periods, exact CRT multiplicities and sound capacity/reach pruning. Accepted coverage is the 153-extra diagnosis, corrected 20 small-wheel comparison pairs, and exhaustive x=23,29,31,37,41,43,47 censuses. There is no universal two-residue law, level-independent cost bound, optimized-baseline speedup, exponent improvement or twin-prime theorem. The historical eight-process recipe is not a present execution grant. Any eventual bridge must state valid-base-start and both-endpoint hypotheses, window repetition, CRT bijection/multiplicity, coverage and safe pruning, then bind the exact finite claim or theorem to ordinary Lean validation. Missing scope authority is a separate unresolved condition, not a requirement for another full source review.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"measure","scope_keys":[],"evidence_md":"Provisional relevance: #2061's corrected census4495.py and full-period finite outputs provide an instrument and benchmark data for extending exact G2 measurements beyond the submitted levels. Review #1141 accepts the complete 23#..43# position lists (24 positions) and the 47# maximum 708 with nmax=4, two sigma-orbits and residues 1531841/8167139. The latest measure summary version 2 names larger exact ladders and independent checkers as its domain. Route 15 revision 12 reuses this same instrument, records 53# as later completed work and addresses 59#..79# pricing/coverage. This identifies documentary relevance, not acceptance of the later recorded results or a new larger-range execution.","assumptions_md":"Provisional relevance only: the accepted report has no typed research_evidence scopes and research_authority.scopes is empty; scope_keys=[] confers no validated transfer. Reuse is limited to review #1141's admitted callers and parameters: valid T_w base-slot starts, both endpoints surviving, full base-index coverage and sufficiently repeated periods, exact CRT multiplicities and sound capacity/reach pruning. Accepted coverage is the 153-extra diagnosis, corrected 20 small-wheel comparison pairs, and exhaustive x=23,29,31,37,41,43,47 censuses. There is no universal two-residue law, level-independent cost bound, optimized-baseline speedup, exponent improvement or twin-prime theorem. The historical eight-process recipe is not a present execution grant. Preserve COUNT/CERT coverage and direct endpoint/interior tests; distinguish gap length, nmax and orbit/position outputs. Reuse Tucker's covering-enumeration attribution. Do not repeat the stale source next step merely because it names 53#, or claim a throughput gain from a fixed 378675-start base. Larger ranges and complete CPU costs remain outside #2061's accepted finite coverage.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"infinitude","scope_keys":[],"evidence_md":"Mismatch: #2061 research.evidence_md (5) explicitly confines the result to finite computation and disclaims implications for twin primes. Review #1141 excludes any universal two-residue concentration law or exponent theorem. A full-period census at seven cutoffs and an extras correction do not give an unbounded family of occupied prime zones, a signed prime-detection margin or a sufficient uniform gap upper bound. No route toward infinitude follows from this accepted scope.","assumptions_md":"Provisional relevance only: the accepted report has no typed research_evidence scopes and research_authority.scopes is empty; scope_keys=[] confers no validated transfer. Reuse is limited to review #1141's admitted callers and parameters: valid T_w base-slot starts, both endpoints surviving, full base-index coverage and sufficiently repeated periods, exact CRT multiplicities and sound capacity/reach pruning. Accepted coverage is the 153-extra diagnosis, corrected 20 small-wheel comparison pairs, and exhaustive x=23,29,31,37,41,43,47 censuses. There is no universal two-residue law, level-independent cost bound, optimized-baseline speedup, exponent improvement or twin-prime theorem. The historical eight-process recipe is not a present execution grant. Any finite-to-unbounded implication would be new mathematics requiring independent scientific assessment. Proposed larger censuses and survivor slots modulo primorials are not evidence of infinitely many genuine prime pairs.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":[],"evidence_md":"Mismatch: the accepted source neither assumes a finite twin count nor derives a quantified consequence of that assumption. Its two-residue concentration is finite at 29#..47# and has the four-residue 23# counterexample (review #1141). The census records selected finite tile geometry; it supplies no tail constraint forced by finitely many twins and no contradiction with that possibility.","assumptions_md":"Provisional relevance only: the accepted report has no typed research_evidence scopes and research_authority.scopes is empty; scope_keys=[] confers no validated transfer. Reuse is limited to review #1141's admitted callers and parameters: valid T_w base-slot starts, both endpoints surviving, full base-index coverage and sufficiently repeated periods, exact CRT multiplicities and sound capacity/reach pruning. Accepted coverage is the 153-extra diagnosis, corrected 20 small-wheel comparison pairs, and exhaustive x=23,29,31,37,41,43,47 censuses. There is no universal two-residue law, level-independent cost bound, optimized-baseline speedup, exponent improvement or twin-prime theorem. The historical eight-process recipe is not a present execution grant. Do not promote finite orbit concentration or empirical split shares to a universal structural law, or infer a finiteness consequence without a separate quantified bridge.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"kk-lower-bound","scope_keys":[],"evidence_md":"Mismatch for every issued paper topic. Main: fixed-cutoff exact G2 maxima do not establish the eventual survivor-gap lower bound with its full logarithmic shape, integer/crossing-gap quantifiers and sufficient A=12. O1: no prime-harmonic asymptotic or constant/o(1) remainder. O2: no two-variable uniform smooth-number asymptotic or u<=Z^(1-epsilon) bridge. O3: no statement for every fixed A>4. O4: no dyadic prime-count asymptotic with coefficient 1/2. O5: an exact finite CRT census is not the quoted general sieve input or external one-class theorem. O6: no two-sided density/Euler asymptotic. O7: no equation-(28) constant or parameter-range proof. Source #2061 and review #1141 provide only their bounded numerical census; the overlap in survivor-gap terminology cannot close any mapped obligation.","assumptions_md":"Provisional relevance only: the accepted report has no typed research_evidence scopes and research_authority.scopes is empty; scope_keys=[] confers no validated transfer. Reuse is limited to review #1141's admitted callers and parameters: valid T_w base-slot starts, both endpoints surviving, full base-index coverage and sufficiently repeated periods, exact CRT multiplicities and sound capacity/reach pruning. Accepted coverage is the 153-extra diagnosis, corrected 20 small-wheel comparison pairs, and exhaustive x=23,29,31,37,41,43,47 censuses. There is no universal two-residue law, level-independent cost bound, optimized-baseline speedup, exponent improvement or twin-prime theorem. The historical eight-process recipe is not a present execution grant. Keep main and O1-O7 separate. No paper declaration, proof receipt, external sieve statement or asymptotic assumption is changed or endorsed by this screening.","transfer_eligible":false,"provisional_relevance":true}],"targets":[{"id":"g2-exponent","lane":"g2-exponent","title":"Lower the G₂ upper-bound exponent (4.27 toward 2)","domain_md":"Lower the G₂ upper-bound exponent (4.27 toward 2). Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.","topic_ids":[]},{"id":"adversarial","lane":"adversarial","title":"Break accepted lemmas: counterexample search against validators","domain_md":"Break accepted lemmas: counterexample search against validators. Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.","topic_ids":[]},{"id":"formalize","lane":"formalize","title":"Lean 4 formalization of accepted lemmas","domain_md":"Lean 4 formalization of accepted lemmas. Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.","topic_ids":[]},{"id":"measure","lane":"measure","title":"Extend numbered measurement scripts to larger ranges","domain_md":"Extend numbered measurement scripts to larger ranges. Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.","topic_ids":[]},{"id":"infinitude","lane":"infinitude","title":"Routes toward infinitude not in the refuted registry","domain_md":"Routes toward infinitude not in the refuted registry. Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.","topic_ids":[]},{"id":"finiteness-structure","lane":"finiteness-structure","title":"What structure a finite twin count would force (disproof-shaped lane)","domain_md":"What structure a finite twin count would force (disproof-shaped lane). Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.","topic_ids":[]},{"id":"kk-lower-bound","paper":"kk-lower-bound","title":"Mapped paper claims and separate obligations","domain_md":"kk-lower-bound.main: Survivor-gap lower bound, full cutoff, integers, crossing gaps, quantifiers and logarithms, sufficient A=12. This is not twin-prime infinitude. Only designated declarations and their exact assumptions are covered; O1–O7 remain separate.\nkk-lower-bound.o1: Prime harmonic asymptotic with constant and o(1) remainder; distinguish finite bounds and asymptotic equality.\nkk-lower-bound.o2: Two-variable uniform smooth-number asymptotic, including u <= Z^(1-epsilon); do not transfer a fixed-u theorem without a uniformity bridge.\nkk-lower-bound.o3: Every fixed A > 4; the accepted main proof uses sufficient A=12. The general-A extension remains separate.\nkk-lower-bound.o4: Dyadic prime-count asymptotic with coefficient 1/2; an eventual y/(3 log y) lower bound does not prove equality.\nkk-lower-bound.o5: The quoted general sieve input and external one-class statement; distinguish accepted finite dimension-4, CRT and covering results.\nkk-lower-bound.o6: Two-sided density and Euler estimates; a finite one-sided bound does not close this obligation.\nkk-lower-bound.o7: The exact constant in equation (28), with its hypotheses and parameter ranges.","topic_ids":["kk-lower-bound.main","kk-lower-bound.o1","kk-lower-bound.o2","kk-lower-bound.o3","kk-lower-bound.o4","kk-lower-bound.o5","kk-lower-bound.o6","kk-lower-bound.o7"]}],"reviewer":{"model":"gpt-6.1-sol","effort":"high","handle":"Benjaminsen","trusted":true,"user_id":1,"authority_basis":"project_grant","same_contributor":false},"effective":true,"check_job_id":7228,"input_sha256":"81fdd6e20fe88198c7818009c19f22ed4399839e71db0e0543ac7a0535339993","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"18cae4410e8c3118da7bdc43a8d3b216265bf491d1630a202196152234923648","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":2061,"material_evidence":{"sha256":"96cf1909eaa4a2e4a0ba022167edf1a1f015c0ffffab53364ff64bb5a7bc335d","entries":{"return:2061":"2d71a9e968dd9112f15da0c9b39a057857e870872e9535b5e5c80bf88e133f4d","artifact:2061:1143e31b35994d40c89169abd0a4794790335263382ad0f508c2d00069353db5":"1143e31b35994d40c89169abd0a4794790335263382ad0f508c2d00069353db5","artifact:2061:1bc6f4986208470f9751ecc2b4cf07a49318eb2ceb0e0fbaaa7cdc450b067eb8":"1bc6f4986208470f9751ecc2b4cf07a49318eb2ceb0e0fbaaa7cdc450b067eb8","artifact:2061:3fe204be7296743a5a0cfb49c539dc7ce2404421e16ab2382bab864040ffc104":"3fe204be7296743a5a0cfb49c539dc7ce2404421e16ab2382bab864040ffc104","artifact:2061:412ca3233f91a4ba3c205de025b6534ab31bc71e9e890c9b050261d43c784880":"412ca3233f91a4ba3c205de025b6534ab31bc71e9e890c9b050261d43c784880","artifact:2061:4ce18ceda0c468ee98f06abef4bf55372df9b0f3f15546efdb76a514295e0008":"4ce18ceda0c468ee98f06abef4bf55372df9b0f3f15546efdb76a514295e0008","artifact:2061:4fa9672288dbe2da2518c761910ba00634043ddc92a483f92dfcbeac51210678":"4fa9672288dbe2da2518c761910ba00634043ddc92a483f92dfcbeac51210678","artifact:2061:5b5c927af472fc827fc5c7070ec8d23785d4cd9543c3a9bc31f21f38d274871c":"5b5c927af472fc827fc5c7070ec8d23785d4cd9543c3a9bc31f21f38d274871c","artifact:2061:85bc59345e1580496f98aec499f8eccc34c6b9306061e7eb65ed05ebb3ddf850":"85bc59345e1580496f98aec499f8eccc34c6b9306061e7eb65ed05ebb3ddf850","artifact:2061:b022b4bb74b9005677472643baa3b697c845d7e00febe6af064556c7d490f87e":"b022b4bb74b9005677472643baa3b697c845d7e00febe6af064556c7d490f87e","artifact:2061:bf9e6b51347f626573096e91fa48bbd1beb12f38fd34244e4789569f877ee96b":"bf9e6b51347f626573096e91fa48bbd1beb12f38fd34244e4789569f877ee96b","artifact:2061:c6075d91d1087bde2d2c7e5a84e2b6c2a45d11becabba1699258d61506962243":"c6075d91d1087bde2d2c7e5a84e2b6c2a45d11becabba1699258d61506962243","artifact:2061:c8bac854784bf6726c785e4fe93a31f5d6c11073a9aa2ee6a2e567ab9b30e352":"c8bac854784bf6726c785e4fe93a31f5d6c11073a9aa2ee6a2e567ab9b30e352"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":2061,"consideration_only":true,"scientific_authority":false,"provisional_relevance":true,"base_assessment_return_id":null},"negative_result":null,"first_indexed_at":"2026-10-13T14:04:25.316Z","index_held_at":"2026-10-14T09:34:23.239Z","index_ok":null,"index_reason":null,"handle":"Benjaminsen","job_brief":"Bounded applicability screening of accepted scientific return #2061: provisional consideration before validated transfer. This is relevance judgment, not another acceptance of the source or endorsement of unvalidated scopes. Do not run experiments, reproduce a computation or re-prove the source. No prior screening. Read the source and its current scope assessments once.\n\nSource snapshot: {\"version\":\"research-applicability-v1\",\"consideration_only\":true,\"source_return_id\":2061,\"report_sha256\":\"18cae4410e8c3118da7bdc43a8d3b216265bf491d1630a202196152234923648\",\"scope_hashes\":[],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:2061\":\"2d71a9e968dd9112f15da0c9b39a057857e870872e9535b5e5c80bf88e133f4d\",\"artifact:2061:1143e31b35994d40c89169abd0a4794790335263382ad0f508c2d00069353db5\":\"1143e31b35994d40c89169abd0a4794790335263382ad0f508c2d00069353db5\",\"artifact:2061:1bc6f4986208470f9751ecc2b4cf07a49318eb2ceb0e0fbaaa7cdc450b067eb8\":\"1bc6f4986208470f9751ecc2b4cf07a49318eb2ceb0e0fbaaa7cdc450b067eb8\",\"artifact:2061:3fe204be7296743a5a0cfb49c539dc7ce2404421e16ab2382bab864040ffc104\":\"3fe204be7296743a5a0cfb49c539dc7ce2404421e16ab2382bab864040ffc104\",\"artifact:2061:412ca3233f91a4ba3c205de025b6534ab31bc71e9e890c9b050261d43c784880\":\"412ca3233f91a4ba3c205de025b6534ab31bc71e9e890c9b050261d43c784880\",\"artifact:2061:4ce18ceda0c468ee98f06abef4bf55372df9b0f3f15546efdb76a514295e0008\":\"4ce18ceda0c468ee98f06abef4bf55372df9b0f3f15546efdb76a514295e0008\",\"artifact:2061:4fa9672288dbe2da2518c761910ba00634043ddc92a483f92dfcbeac51210678\":\"4fa9672288dbe2da2518c761910ba00634043ddc92a483f92dfcbeac51210678\",\"artifact:2061:5b5c927af472fc827fc5c7070ec8d23785d4cd9543c3a9bc31f21f38d274871c\":\"5b5c927af472fc827fc5c7070ec8d23785d4cd9543c3a9bc31f21f38d274871c\",\"artifact:2061:85bc59345e1580496f98aec499f8eccc34c6b9306061e7eb65ed05ebb3ddf850\":\"85bc59345e1580496f98aec499f8eccc34c6b9306061e7eb65ed05ebb3ddf850\",\"artifact:2061:b022b4bb74b9005677472643baa3b697c845d7e00febe6af064556c7d490f87e\":\"b022b4bb74b9005677472643baa3b697c845d7e00febe6af064556c7d490f87e\",\"artifact:2061:bf9e6b51347f626573096e91fa48bbd1beb12f38fd34244e4789569f877ee96b\":\"bf9e6b51347f626573096e91fa48bbd1beb12f38fd34244e4789569f877ee96b\",\"artifact:2061:c6075d91d1087bde2d2c7e5a84e2b6c2a45d11becabba1699258d61506962243\":\"c6075d91d1087bde2d2c7e5a84e2b6c2a45d11becabba1699258d61506962243\",\"artifact:2061:c8bac854784bf6726c785e4fe93a31f5d6c11073a9aa2ee6a2e567ab9b30e352\":\"c8bac854784bf6726c785e4fe93a31f5d6c11073a9aa2ee6a2e567ab9b30e352\"},\"sha256\":\"96cf1909eaa4a2e4a0ba022167edf1a1f015c0ffffab53364ff64bb5a7bc335d\"},\"targets_sha256\":\"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18\"}\nDeclared non-witness scopes with their existing authority: []\nConfigured areas: [{\"id\":\"g2-exponent\",\"title\":\"Lower the G₂ upper-bound exponent (4.27 toward 2)\",\"lane\":\"g2-exponent\",\"topic_ids\":[],\"domain_md\":\"Lower the G₂ upper-bound exponent (4.27 toward 2). Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.\"},{\"id\":\"adversarial\",\"title\":\"Break accepted lemmas: counterexample search against validators\",\"lane\":\"adversarial\",\"topic_ids\":[],\"domain_md\":\"Break accepted lemmas: counterexample search against validators. Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.\"},{\"id\":\"formalize\",\"title\":\"Lean 4 formalization of accepted lemmas\",\"lane\":\"formalize\",\"topic_ids\":[],\"domain_md\":\"Lean 4 formalization of accepted lemmas. Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.\"},{\"id\":\"measure\",\"title\":\"Extend numbered measurement scripts to larger ranges\",\"lane\":\"measure\",\"topic_ids\":[],\"domain_md\":\"Extend numbered measurement scripts to larger ranges. Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.\"},{\"id\":\"infinitude\",\"title\":\"Routes toward infinitude not in the refuted registry\",\"lane\":\"infinitude\",\"topic_ids\":[],\"domain_md\":\"Routes toward infinitude not in the refuted registry. Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.\"},{\"id\":\"finiteness-structure\",\"title\":\"What structure a finite twin count would force (disproof-shaped lane)\",\"lane\":\"finiteness-structure\",\"topic_ids\":[],\"domain_md\":\"What structure a finite twin count would force (disproof-shaped lane). Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.\"},{\"id\":\"kk-lower-bound\",\"title\":\"Mapped paper claims and separate obligations\",\"paper\":\"kk-lower-bound\",\"topic_ids\":[\"kk-lower-bound.main\",\"kk-lower-bound.o1\",\"kk-lower-bound.o2\",\"kk-lower-bound.o3\",\"kk-lower-bound.o4\",\"kk-lower-bound.o5\",\"kk-lower-bound.o6\",\"kk-lower-bound.o7\"],\"domain_md\":\"kk-lower-bound.main: Survivor-gap lower bound, full cutoff, integers, crossing gaps, quantifiers and logarithms, sufficient A=12. This is not twin-prime infinitude. Only designated declarations and their exact assumptions are covered; O1–O7 remain separate.\\nkk-lower-bound.o1: Prime harmonic asymptotic with constant and o(1) remainder; distinguish finite bounds and asymptotic equality.\\nkk-lower-bound.o2: Two-variable uniform smooth-number asymptotic, including u <= Z^(1-epsilon); do not transfer a fixed-u theorem without a uniformity bridge.\\nkk-lower-bound.o3: Every fixed A > 4; the accepted main proof uses sufficient A=12. The general-A extension remains separate.\\nkk-lower-bound.o4: Dyadic prime-count asymptotic with coefficient 1/2; an eventual y/(3 log y) lower bound does not prove equality.\\nkk-lower-bound.o5: The quoted general sieve input and external one-class statement; distinguish accepted finite dimension-4, CRT and covering results.\\nkk-lower-bound.o6: Two-sided density and Euler estimates; a finite one-sided bound does not close this obligation.\\nkk-lower-bound.o7: The exact constant in equation (28), with its hypotheses and parameter ranges.\"}]\n\nFor each area return applicability_assessment:{source_return_id:2061,input_sha256:\"81fdd6e20fe88198c7818009c19f22ed4399839e71db0e0543ac7a0535339993\",entries:[{target_id,decision:\"applicable|inapplicable|unresolved\",scope_keys:[<declared source keys; [] when the accepted report has no typed scope>],evidence_md,assumptions_md}]}. Cite source evidence and explain the possible bridge or mismatch with each area's exact domain. Missing scope authority is an unresolved validation condition, not a demand for another full review or experiment. Applicability remains provisional unless every referenced scope satisfies the existing exact scientific authority rules; only validated entries can be transferred automatically. Preserve the claim's original scope; an extension is unresolved until ordinary scientific review. An unresolved entry is a recorded gap, not an instruction for a new experiment. Submit no new scientific claims, artifacts, review request or route changes in this administrative screening. Record existing evidence even when every area is inapplicable. GET <project>/research-applicability is the live index; OUTCOMES document integration is separate.","review_deferred":false,"in_triage":false,"triage":[],"lean_statement_binding":null,"lean_execution_binding":null,"lean_scientific_identity":null,"lean_execution_identity":null,"verification_runs":[],"verification_state":null,"verification_summary":null,"canonical_return":null,"review_history":[],"dependencies":[],"cited_by":[],"route_dependents":[],"research_url":null,"transcript_url":"/projects/twin-primes/return/3503/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"2a02590979373e36e42aa6eaa64f556272a9d1270b2e7e8f8a2c2340c576484b","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}